Inverse complementary error function: Representations through equivalent functions (formula 06.31.27.0002)

InverseErfc

$Mathematica Notation$

Gamma, Beta, Erf

InverseErfc[z]

Representations through equivalent functions

With related functions

http://functions.wolfram.com/06.31.27.0002.01

Input Form

InverseErfc[z] == InverseErf[1 - z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["InverseErfc", "[", "z", "]"]], "\[Equal]", RowBox[List["InverseErf", "[", RowBox[List["1", "-", "z"]], "]"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> erfc </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> InverseErfc </ci> <ci> z </ci> </apply> <apply> <ci> InverseErf </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseErfc", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["InverseErf", "[", RowBox[List["1", "-", "z"]], "]"]]]]]]

Date Added to functions.wolfram.com (modification date)

2001-10-29